Buy all the medicines you are likely to need BEFORE your baby needs them and unwrap all the packaging (nothing worse than having to drag a cranky baby to the store or trying to fumble through the packaging with one hand while you hold a fussy baby in the other!).

Liquid medicine measure that looks like a syringe-- I hate those bulb-types!-- and the syringe holds more medicine so I can get a full dose with one measure.

Gas drops for babies-- REALLY good to have on hand and can be given to newborns.

Plastic links-- they're great! DS liked playing with them/teething but they were really handy because you could "link" toys to a chain of links and then "link" the chain to most anything (stroller, grocery cart) and the toys wouldn't get lost when kiddo dropped them. We would also put a receiving blanket over the grocery cart bar and then put the link chain over it to keep kiddo from touching the bar.

Old towels-- we kept a towel spread out at the foot of our bed to change baby on. If anything "escaped", we just needed to wash the towel (not the comforter).

Lap pads. Before DS started rolling over, we just laid one in his bassinet-- when he'd spit up, we'd just switch out the lap pad for a clean one (otherwise we would have been changing the sheet at least daily!).

Plain frozen bagels for teething. They are really great because after we feed DS, we keep him in his highchair at the table and give him 1/4 of a frozen bagel-- then DH and I can actually eat our dinners at the same time! :) Just an FYI-- you do need to really watch as the bagel starts to thaw-- otherwise, they can break off pieces big enough to choke on.

Like the last poster mentioned, buying all the medicines BEFORE you need it is soooo key. The gas drops, plastic links and lap pads were hits with us too.

Having a humidifer on hand BEFORE you actually need one.

The bulb syringe from the hospital, otherwise known as the Big Green Monster. (LOL) That thing works SO much better than those ones you buy in the store. Also, nasal spray stuff that helps loosen boogies. That stuff is priceless.

Exersaucer!!

Baby Bjorn - very handy

Dishwasher basket(s) to hold and wash all the nipples, collars, pacifiers, and now sippy cup parts.

If you don't have a dishwasher, get the bottle drying rack. I love mine.
A bouncer/vibrating chair for baby or a swing. The swing has worked some miracles when dd is cranky.
Cloth diapers for burp cloths.
Bib that just fit over baby's head (no velcro or snaps) so they actually stay on for the constant drooler.
Any diaper rash cream.
I would also definitely get any and all medications you may need before baby gets sick. Make sure you check the expiration dates before you buy them so you know you won't be wasting your money if baby doesn't need it within a few months.
A little plush toy connected to a rattle ring. She has played with that one all the time.
I would also buy a pack of diapers that are one size larger than baby currently wears and always have one bag of current size diapers on hand. Nothing like going to the store with baby and a makeshift diaper on her;)

1) Diaper Genie (we have one upstairs and one downstairs)
2) Extra pacifiers
3) Bouncy seat (We were given two at the shower, so have one upstairs and one downstairs. Of the two, the one with carrying straps is MUCH better, and sooo much easier to carry around from room to room)
4) Plastic links are AWESOME...for exactly the reasons Magdelena stated (get more than one set and use them everywhere!)
5) Our diaper bag is not a diaper bag at all, but a JanSport Mega Student backpack. We can carry sooo much stuff in that thing!! The straps are really comfy. Our family is active, so it comes in handy for corraling all DS's stuff during our outdoor activities...and when he's through with diapers, we will be able to use it for other things.

Our most helpful item has been this (safe) porta-crib we found at a garage sale. It has a mattress pad that is height adjustable and has wheels so I can move all around the house (oh, also wood floors are great). We used it as a crib next to our bed when my son was a newborn, and still use it as a playpen - - - either with the bouncy seat in it (elevated so he can see us better - for instance at the table) or lying in it with the swinging toy gym over his head. He spends lots of time with me in the kitchen and will play in it while I make breakfast and dinner. Then, zoom! we're off to another room to fold laundry and he'll play some more next to a window.

A really GOOD pair of baby fingernail scissors
(anything sold in a bubble pack is not thin enough or sharp enough; we got the Denco brand from the cutlery-quality scissors kiosk at our full-service pharmacy.)

a nursing pillow--not a rounded one, a flat one
Made a HUGE difference; I had three friends who suffered through nursing, finding it hard to hold their babies up high enough to meet the breast, until I loaned them mine. Nojo doesn't make it any more; My Brest friend is the closest I've seen, though I'm skeptical about the strap around the back and think I personally would find it annoying. I think I'd like it better than the Boppy because the Boppy is rounded; I used to just lay my baby directly on the flat surface of the nursing pillow and lay my arm behind her back; I'd be afraid of the baby rolling off the Boppy. Plus the Brest Friend can be made to slope up toward the baby's head, so the head is higher than the torso, and I liked that about my nursing pillow.

Baby Bjorn
Had a Snugli w/ the first baby and hated it; went out and got a Baby Bjorn.

Breast pump
If I had it to do over, I'd have purchased a Medela Lactina for $400 or so, used it for the full year that I rented one, loaned it to friends and relatives (if I asked them for a $25 donation to help cover the costs, they'd have thought it a huge bargain), used it to feed Baby No. 2 a Preemie, then sold it used. I'd have still come out ahead. I got the Pump-in-Style for Baby No. 2, and it's pretty wimpy compared w/ the Lactina (which I loved)

Baby sleeping bag. Ours has a hood and we love it! DS's room can get a little cool-- with the sleeping bag we don't worry about him getting too cold when he kicks the covers off.

Infant car seat with the lift-out carrier. We started off in the 8-40 lb. standard model-- what a pain! The carrier was great because you wouldn't have to wake kiddo to take him inside and because it was so handy for hooking on grocery carts and to give him a place to be when we went out to eat. :)

For next time-- if weather will be at all cold during child's 1st 6 months-- we'll get a carrier cover-- every mom I know that has one raves about them (don't have to mess with bunting outfits, etc.).

Oh, yes, the fleece carseat carrier covers are WONDERFUL!! We never used a bunting when DD was tiny. We just used the cover and it had a little flap you could open or close over the baby's face. (Even when closed, it is not totally closed. They can breathe just fine.)

BABY BACKPACK - for when baby is old enough to sit up by him/herself. Holy cow - we've just started using one and it has been a godsend! DS will ride along happily for *hours* in it. (This from a kid who will not sit alone for more than 29 seconds at a time!) I use it indoors while cleaning - especially for things like vacuuming, dusting, cleaning countertops (i.e. things you don't have to bend over for, although it is good training for bending correctly - you have to use your legs!) and outdoors for long walks. I highly recommend this item - my house is finally clean again and I'm getting in pretty good shape!